Question: Simplify the following expression: $k = \dfrac{4fg + 5g^2}{2fg + g} - \dfrac{fg}{2fg + g}$ You can assume $f,g,h \neq 0$.
Answer: Since the expressions have the same denominator we simply combine the numerators: $k = \dfrac{4fg + 5g^2 - (fg)}{2fg + g}$ $k = \dfrac{3fg + 5g^2}{2fg + g}$ The numerator and denominator have a common factor of $g$, so we can simplify $k = \dfrac{3f + 5g}{2f + 1}$